The Broadway graveyard is full of flops that had great scores and bad scripts.

An outstanding example is the 1965 musical “On a Clear Day You Can See Forever.”

The score — music by Burton Lane, lyrics by Alan Jay Lerner — is melodic, witty and whimsical; the title song became a standard when Barbra Streisand recorded it for the 1970 movie.

But Lerner’s original story — about extrasensory perception, reincarnation and transmutation — is as loony as he was (more on that in a minute).

As one critic wrote, “What Mr. Lerner should have worried about was not another life but a better idea.”

Director Michael Mayer (“American Idiot”) and playwright Peter Parnell may have come up with that “better idea.”

Their version of “On a Clear Day” is being given a staged reading this weekend by New York Stage and Film, a production company based at Vassar College. Mayer and Parnell have been coy about the changes they’ve made.

But what good’s a gossip column that doesn’t spill the beans every now and then?

Here’s the skinny:

In the original, the main character was a kooky young woman who, in a past life, was an English aristocrat.

In the new version, the young woman is a young man who, in a past life, was a black female jazz singer.

Gender-bending is hardly a new concept in the theater — see “Twelfth Night” by William Shakespeare — but this new twist on “Clear Day” already has impressed the Vineyard Theatre. The off-Broadway company will present a full-scale production in January.

In the meantime, I thought it would be fun to find out just how nutty the old version was. So I called up its leading man, Tony winner John Cullum, who’s opening on Broadway this fall in “The Scottsboro Boys.”

“It was a crazy, wild experience,” he recalled.

During the show’s Boston tryout, Cullum replaced Louis Jordan, who was playing a Viennese psychiatrist.

Jordan, Cullum says, was “being wiped out” by his leading lady, Barbara Harris.

The actor had no idea he was being fired. The producers sent him off on a two-week vacation, ostensibly to learn some new scenes, and never brought him back.

When Cullum took over the role, he discovered that Jordan had a secret: He didn’t know his lines.

“The first time I was onstage, I realized that Louis had written the lines all over the set,” Cullum says. “If I opened the cigarette case or a drawer, there would be the lines, written out. Except the script kept changing. So the lines all over the set were different from the lines I was trying to learn.”

The script was a mess because the author was, too.

Lerner was living on his yacht in the Charles River. One of his guests was Max Jacobson, better known as “Dr. Feelgood.”

The good doctor was giving Lerner shots of something that was supposed to eliminate sleep and stimulate the imagination.

A musical about ESP was being written by a guy on LSD.

“Alan could stay up for hours and hours working on the show,” says Cullum. “He told me he’d written 2,500 pages of dialogue. But it wasn’t inspired writing. It was just writing for the sake of writing.

“He was up and then — BOOM! — he’d pass out, right in front of you. When he was up, he’d disappear. We’d come to rehearsal in the morning and find out he’d gone to California or Europe. He’d just get on a plane and go see somebody. So even though he was writing the show, I never had much contact with him.”

“She loved to improvise,” Cullum says. “If I had a line — ‘Why are you smiling?’ — she’d frown. It was charming, but it was difficult. I had to do a Viennese accent, and while I could do improvisations, I couldn’t do them with a Viennese accent. So I was locked into the script, and she was floating all over the place.

“Barbara was a great talent. One of the best I’ve ever worked with. But she was always on the verge of something. She never actually went bananas, but there was something lurking there, something very dark.”

“On a Clear Day” opened at the Mark Hellinger Theatre with what was then the priciest ticket on Broadway — $11.90.

Despite tepid reviews, the production managed to eke out an eight-month run.

“We’d gotten pretty good by then,” says Cullum. “But Alan had lost heart. Everybody was saying this is no ‘Camelot’ or ‘My Fair Lady.’ He said, ‘Just close it.’

“I hope the new version works,” Cullum adds. “Some of Alan’s ideas were wonderful, and the music is gorgeous.”